Chapter 10: Q27. (page 661)

Find $m ∠ X$ to the nearest degree.

Short Answer

Expert verified

Measure of angle $X$ to the nearest degree is given as,

$m ∠ X = 37 °$

Step by step solution

Step 1. Define the trigonometric ratio ‘sinθ’.

If $θ$ is any angle in a given right angle triangle, then the trignometric ratio is given as,

$\sin θ = \frac{length of side opposite to ∠ θ}{length of hypotenuse}$

Step 2. Calculate the measure of angle X (m∠X).

Observe the figure.

From the figure, $X Z$ is hypotenuse (side opposite to 90 degree) and length of $X Z$ is 15 units.

$Y Z$ is side opposite to angle $X$ and the length of $Y Z$ is 9 units.

$\begin{array}{l} \sin X = \frac{length of side opposite to ∠ X}{length of hypotenuse} \\ \sin X = \frac{length of YZ}{length of XZ} \\ \sin X = \frac{9}{15} \\ \sin X = 0.6 \\ X = \sin^{- 1} (0.6) \\ X = 36.87 ° \end{array}$

Step 3. State the conclusion.

The measure of angle $X$ is $36.87 °$ .

Here, role="math" localid="1647930486163" $36 .87 ° \approx 37 ° [Rounding to the nearest degree]$ .

Therefore, measure of angle $X$ $(m ∠ X)$ to the nearest degree is $37 °$ .

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Find $m ∠ X$ to the nearest degree.

Short Answer

Step by step solution

Step 1. Define the trigonometric ratio ‘sinθ’.

Step 2. Calculate the measure of angle X (m∠X).

Step 3. State the conclusion.

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Find m∠Xto the nearest degree.

Short Answer

Step by step solution

Step 1. Define the trigonometric ratio ‘sinθ’.

Step 2. Calculate the measure of angle X (m∠X).

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Decision Maths

Calculus

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find $m ∠ X$ to the nearest degree.